COVID-19 is primarily a respiratory disease, but numerous studies have indicated the involvement of various organ systems during the course of illness. We conducted a comprehensive review of atypical complications of COVID-19 with their incidence range (IR) and their impact on hospitalization and mortality rates. We identified 97 studies, including 55 research articles and 42 case studies. We reviewed four major body organ systems for various types of atypical complications: (i) Gastro-intestinal (GI) and hepatobiliary system, e.g., bowel ischemia/infarction (IR: 1.49–83.87%), GI bleeding/hemorrhage (IR: 0.47–10.6%), hepatic ischemia (IR: 1.0–7.4%); (ii) Neurological system, e.g., acute ischemic stroke/cerebral venous sinus thrombosis/cerebral hemorrhage (IR: 0.5–90.9%), anosmia (IR: 4.9–79.6%), dysgeusia (IR: 2.8–83.38%), encephalopathy/encephalitis with or without fever and hypoxia (IR: 0.19–35.2%); (iii) Renal system, e.g., acute kidney injury (AKI)/acute renal failure (IR: 0.5–68.8%); (iv) Cardiovascular system, e.g., acute cardiac injury/non-coronary myocardial injury (IR: 7.2–55.56%), arrhythmia/ventricular tachycardia/ventricular fibrillation (IR: 5.9–16.7%), and coagulopathy/venous thromboembolism (IR: 19–34.4%). This review encourages and informs healthcare practitioners to keenly monitor COVID-19 survivors for these atypical complications in all major organ systems and not only treat the respiratory symptoms of patients. Post-COVID effects should be monitored, and follow-up of patients should be performed on a regular basis to check for long-term complications.